The Rays selected Tapia's contract from Triple-A Durham on Saturday, Marc Topkin of the Tampa Bay Times reports.
With Brandon Lowe (knee) on the injured list and facing an extended absence, Tapia will be added to the roster to give the team an extra bat off the bench. Tapia has slashed .230/.308/.338 with 13 RBI across 157 plate appearances with the Red Sox and Brewers this season.